Measurements of Some Gamma-Ray Relative Intensities and Internal
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Iowa State University Capstones, Theses and Retrospective Theses and Dissertations Dissertations 1967 Measurements of some gamma-ray relative intensities and internal conversion coefficients using a bent-crystal monochromator Gerald Clifford Nelson Iowa State University Follow this and additional works at: https://lib.dr.iastate.edu/rtd Part of the Nuclear Commons Recommended Citation Nelson, Gerald Clifford, "Measurements of some gamma-ray relative intensities and internal conversion coefficients using a bent- crystal monochromator " (1967). Retrospective Theses and Dissertations. 3198. https://lib.dr.iastate.edu/rtd/3198 This Dissertation is brought to you for free and open access by the Iowa State University Capstones, Theses and Dissertations at Iowa State University Digital Repository. It has been accepted for inclusion in Retrospective Theses and Dissertations by an authorized administrator of Iowa State University Digital Repository. For more information, please contact [email protected]. This dissertation has been microfihned exactly as received 6 8-596 9 NELSON, Gerald Clifford, 1940- MEASUREMENTS OF SOME GAMMA-RAY RELATIVE INTENSITIES AND INTERNAL CONVERSION COEFFICIENTS USING A BENT-CRYSTAL MONOCHROMATOR. Iowa State University, Ph,D., 1967 Physics, nuclear University Microfilms, Inc., Ann Arbor. Michigan MEASUREMENTS OF SOME GAMMA-RAY RELATIVE INTENSITIES AND INTERNAL CONVERSION COEFFICIENTS USING A BENT-CRYSTAL MONOCHROMATOR by Gerald Clifford Nelson A Dissertation Submitted to the Graduate Faculty in Partial Fulfillment of The Requirements for the Degree of DOCTOR OF PHILOSOPHY Major Subject: Physics Approved: Signature was redacted for privacy. In Charge of Major Work Signature was redacted for privacy. Department Signature was redacted for privacy. Iowa State University Of Science and Technology Ames, Iowa 1967 il TABLE OF CONTENTS Page ABSTRACT I. INTRODUCTION 1 A. Definition of the Internal Conversion Process 1 B. Remarks About Internal Conversion Coefficients 3 C. Experimental Methods of Measuring Internal Conversion Coefficients 6 D. Some Experimental Methods of Measuring Gamma-Ray Relative Intensities 8 II. THEORY OF THE LINEAR LEAST-SQUARES SCINTILLATION METHOD 18 III. EXPERIMENTAL EQUIPMENT AND METHODS 23 IV. MEASUREMENTS AND RESULTS 38 A. Internal Conversion Coefficients of the E2 Transitions in Yb^^O and Er^^^ 38 1. Internal conversion coefficient of the 84.3-keV transition in Yb^^^ , 38 2. Internal conversion coefficient of the 80.6-keV transition in Er^^^ 49 3. Discussion of the E2 internal conversion coefficients in Yb^^O and Er^^^ 56 B. Internal Conversion Coefficients in Hf^^^ 57 180 1. Analysis of the Hf X-ray and gamma-ray spectrum 59 2. Results and discussion 71 C. K Internal Conversion Coefficients in Gd^^^ 76 1. Analysis of the Gd^^^ X-ray and gamma-ray spectrum 76 2. Results and discussion 84 D. Relative Intensities of the 104-, 142- and 246-keV 1RA Gamma Rays in Eu 86 iii 155 Page 1. Analysis of the Eu gamma-ray spectrum 87 2. Results and discussion 90 E. Concluding Remarks 96 V. LITERATURE CITED 98 VI. ACKNOWLEDGMENTS 103 VII. APPENDIX A: EFFECTS DUE TO SOURCE WIDTH AND POSITION 104 VIII. APPENDIX B: CALCULATION OF THE EFFICIENCY OF THE NAI CRYSTAL 110 IX. APPENDIX C: DERIVATION OF THE ERRORS ASSOCIATED WITH THE LINEAR LEAST-SQUARES PROCEDURE 121 X. APPENDIX D: FLOW CHART AND REVISED COMPUTER PROGRAM 137 iv ABSTRACT The X-ray and gamma-ray relative intensities were measured, from the decay of and Sm^^^ with a bent-crystal mono- chromator and a linear least-squares computer program. The K-shell internal conversion coefficients were determined for the E2 transitions in and Er . The K-shell conversion coefficient, for the 84.3-keV transition in Yb^^^ was determined to be 1.43±0.04 while the K-shell internal conver sion coefficient for the 80.6-keV transition in Er was determined to be 4* + 1.72±0.06. The results for these 2 -K) transitions are five percent higher than the theoretical values for these transitions. From the relative inten- 180 sities of the transitions in Hf it was possible to deduce a value for the 93 total internal conversion coefficient for the 93.3-keV transition of cy = 4.91±0.23. Using the previous measurements of conversion electron intensi ties of Edwards and Boehm and the present measured gamma-ray relative inten sities, internal conversion coefficients for all the other transitions were obtained. The present measurements of for the 215.3-, 332.5- and 443.8- keV E2 transitions are 11 percent lower than the theoretical values, while for the 93.3-keV E2 transition agrees closely with the theoretical value. These results are in close agreement with the previous measurements of Edwards and Boehm. The present valjie_for_a|^ for the 501-keV transition agrees closely with the theoretical for an E3 multipolarity. From the 1 CC X-ray and gamma-ray relative intensities of the transitions in Gd and the previous measurement of the ratio of K conversion electrons for the 86- and 105-keV transitions of Subba Rao, it was possible to determine the K V conversion coefficients for the 86- and 105-keV transitions of «j, = 0.43 ±0.06 and = 0.23±0.03. These results are in agreement with the theo retical values for pure El transitions. The relative intensities of the 246-, 142- and 104-keV gamma rays following the decay of 22 minute were determined with improved precision in order that they might be used to determine accurately the conversion coefficients for these transitions. 1 I. INTRODUCTION A. Definition of the Internal Conversion Process Below 1-MeV the principal processes by which an excited nucleus can make a transition to a lower energy level are gamma-ray emission and inter nal conversion. In the first process the nucleus emits a gamma ray with energy equal to the transition energy, N*->-N+Y where N* is the nucleus in the excited state, N is the nucleus in the lower energy state and y is the emitted gamma ray which has an energy equal to the transition energy. In internal conversion the nuclear transition energy is transferred to one of the orbital electrons by a direct interaction be tween the electron and the charged nucléons. The electron is then ejected from the atom with an energy equal to the nuclear transition energy minus the binding energy of the electron. N*+Ze - N+(Z-l)e + e continuum ~ ^N*-N " ^binding where N* +Ze is the excited nucleus with Z electrons, N + (Z-l)e is the nucleus in the lower energy state with Z-1 electrons, is the ejected electron in the continuum, is the energy of the ejected electron, E^*_^ is the transition energy and is the binding energy of the ejected electron. Following the ejection of an internal conversion electron, the atomic electrons will readjust, and an outer electron will fill the vacancy. The energy difference is carried off by one of two processes. The first and predominant process is the emission of an X-ray which will have an energy equal to the difference between the binding energy of the shell in which the vacancy occurred and the binding energy of the shell from which the outer electron came. The other process by which energy is carried off following internal conversion is the emission of a second electron called an Auger electron. The resulting atom is ionized in two shells. The energy of the emitted electron is approximately given by E (KXY) = E (K) - E (X) - E^ (Y) = E (K) - E^ (X) - E (Y), where K, X, and Y are respectively the shell from which the internal conver sion electron is ejected, the shell from which the K shell is filled, and the shell from which the Auger electron is emitted. E^ (Y) is the electron binding energy of the Y shell in an atom with charge Z ionized in the X shell. For a given transition the internal conversion coefficient, a, is de fined as the ratio of N^, the number of internal conversion electrons emitted per unit time, to N^, the number of gamma rays emitted per unit time, " = lit • The internal conversion coefficient for a particular shell or subshell is defined similarly. For the K shell n5 3 |/ where is the number of internal conversion electrons emitted from the K shell per unit time. The total internal conversion coefficient is the sum of the internal conversion coefficients of the individual shells. B. Remarks About Internal Conversion Coefficients The internal conversion coefficients depend strongly on five para meters; the shell in which the conversion occurs, the transition energy, the atomic number, the angular momentum change and the parity change between the initial and final nuclear states. Internal conversion coefficients always increase as the transition energy decreases. They normally increase with Z, and always increase as the angular momentum, L, increases. To a large ex tent, internal conversion coefficients are independent of detailed nuclear structure. This makes it possible to obtain information about the spin and parity of the nuclear transition by comparing the experimentally determined conversion coefficients with those theoretically predicted. When the nuclear angular momenta for initial and final states are and J^, the emitted gamma ray can have any angular momentum L for which AJ = . The electromagnetic transitions are classified as electric 2^, EL, or mag netic 2^, ML, if the parity change between the initial and final nuclear states is (-1)'" or (-1)'"^^, respectively. The internal conversion coefficient is in general a mixture of 4 conversion coefficients of pure angular momentum L a = I ' where % a, =1. L ^ The aj^ represent the fraction of total gamma rays emitted with angular mo mentum L. For a given type of multipole, the relative intensity for multi- poles with L and L+2 is given by (1) ' - 1.